Properties

Label 2842.e
Number of curves $2$
Conductor $2842$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2842.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2842.e1 2842e2 \([1, 0, 0, -22296, 1288244]\) \(-10418796526321/82044596\) \(-9652464674804\) \([]\) \(7200\) \(1.3201\)  
2842.e2 2842e1 \([1, 0, 0, 244, -2416]\) \(13651919/29696\) \(-3493704704\) \([]\) \(1440\) \(0.51540\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2842.e have rank \(1\).

Complex multiplication

The elliptic curves in class 2842.e do not have complex multiplication.

Modular form 2842.2.a.e

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + q^{8} - 2 q^{9} - q^{10} - 3 q^{11} + q^{12} + q^{13} - q^{15} + q^{16} - 8 q^{17} - 2 q^{18} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.